Simplify to lowest terms. $\dfrac{112}{140}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 112 and 140? $112 = 2\cdot2\cdot2\cdot2\cdot7$ $140 = 2\cdot2\cdot5\cdot7$ $\mbox{GCD}(112, 140) = 2\cdot2\cdot7 = 28$ $\dfrac{112}{140} = \dfrac{4 \cdot 28}{ 5\cdot 28}$ $\hphantom{\dfrac{112}{140}} = \dfrac{4}{5} \cdot \dfrac{28}{28}$ $\hphantom{\dfrac{112}{140}} = \dfrac{4}{5} \cdot 1$ $\hphantom{\dfrac{112}{140}} = \dfrac{4}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{112}{140}= \dfrac{2\cdot56}{2\cdot70}= \dfrac{2\cdot 2\cdot28}{2\cdot 2\cdot35}= \dfrac{2\cdot 2\cdot 7\cdot4}{2\cdot 2\cdot 7\cdot5}= \dfrac{4}{5}$